4. What is the solution of the system of equations? y=-2x+5 y=-2x+20
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![-20 \leq 3x+1 \leq 10\\ \Rightarrow\ -21 \leq 3x \leq 9\\ \Rightarrow\ -7 \leq x \leq 3\\ Sol=[-7\ 3]\ if\ x\ is\ a\ real. ](https://tex.z-dn.net/?f=-20%20%5Cleq%203x%2B1%20%5Cleq%2010%5C%5C%0A%5CRightarrow%5C%20-21%20%5Cleq%203x%20%5Cleq%209%5C%5C%0A%5CRightarrow%5C%20-7%20%5Cleq%20x%20%5Cleq%203%5C%5C%0A%0ASol%3D%5B-7%5C%203%5D%5C%20if%5C%20x%5C%20is%5C%20a%5C%20real.%0A)
Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, the parameters are:
The lower limit of this interval is:
The upper limit of this interval is:
The 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.
More can be learned about the z-distribution at brainly.com/question/25890103